The sum of two numbers is $70$, and their difference is $14$. What are the two numbers?
Solution: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 70}$ ${x-y = 14}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 84 $ $ x = \dfrac{84}{2} $ ${x = 42}$ Now that you know ${x = 42}$ , plug it back into $ {x+y = 70}$ to find $y$ ${(42)}{ + y = 70}$ ${y = 28}$ You can also plug ${x = 42}$ into $ {x-y = 14}$ and get the same answer for $y$ ${(42)}{ - y = 14}$ ${y = 28}$ Therefore, the larger number is $42$, and the smaller number is $28$.